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Rigidity and the lower bound theorem 1
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/cpa.3160210203openalex-snapshot
Geometrical problems concerning polyhedra in the large
inferredcites →https://doi.org/10.1002/sapm1975542135openalex-snapshot
The Upper Bound Conjecture and Cohen‐Macaulay Rings
inferredcites →https://doi.org/10.1007/978-1-4612-1148-8openalex-snapshot
An Introduction to Convex Polytopes
inferredcites →https://doi.org/10.1007/978-1-4899-6752-7openalex-snapshot
Combinatorics and Commutative Algebra
inferredcites →https://doi.org/10.1007/978-3-642-65609-5openalex-snapshot
Vorlesungen über die Theorie der Polyeder
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Partial Differential Relations
inferredcites →https://doi.org/10.1007/bf01218376openalex-snapshot
On the number of faces of simplicial complexes and the purity of Frobenius
inferredcites →https://doi.org/10.1007/bf02162086openalex-snapshot
A comparison of primal and dual methods of linear programming
inferredcites →https://doi.org/10.1007/bf02391774openalex-snapshot
Sur la formule de Siegel dans la théorie des groupes classiques
inferredcites →https://doi.org/10.1007/bf02392139openalex-snapshot
Polytope pairs and their relationship to linear programming
inferredcites →https://doi.org/10.1007/bf02392331openalex-snapshot
The lower bound conjecture for 3- and 4-manifolds
inferredcites →https://doi.org/10.1007/bf02684342openalex-snapshot
A counterexample to the rigidity conjecture for polyhedra
inferredcites →https://doi.org/10.1007/bf02771471openalex-snapshot
The numbers of faces of simplicial polytopes
inferredcites →https://doi.org/10.1007/bf02771522openalex-snapshot
The minimum number of vertices of a simple polytope
inferredcites →https://doi.org/10.1007/bf02937351openalex-snapshot
Quotient polytopes of cyclic polytopes part I: Structure and characterization
inferredcites →https://doi.org/10.1007/bf03026567openalex-snapshot
The 9-vertex complex projective plane
inferredcites →https://doi.org/10.1007/bfb0060102openalex-snapshot
On Steinitz's theorem concerning convex 3-polytopes and on some properties of planar graphs
inferredcites →https://doi.org/10.1007/bfb0066118openalex-snapshot
Almost all simply connected closed surfaces are rigid
inferredcites →https://doi.org/10.1016/0001-8708(80)90037-7openalex-snapshot
The rigidity of certain cabled frameworks and the second-order rigidity of arbitrarily triangulated convex surfaces
inferredcites →https://doi.org/10.1016/0001-8708(80)90050-xopenalex-snapshot
The number of faces of a simplicial convex polytope
inferredcites →https://doi.org/10.1016/0022-247x(79)90108-2openalex-snapshot
The rigidity of graphs, II
inferredcites →https://doi.org/10.1016/0040-9383(80)90003-8openalex-snapshot
Intersection homology theory
inferredcites →https://doi.org/10.1016/0040-9383(88)90004-3openalex-snapshot
Triangulating 3-manifolds using 5 vertex link types
inferredcites →https://doi.org/10.1016/0097-3165(73)90074-5openalex-snapshot
Neighborly 4-polytopes with 9 vertices
inferredcites →https://doi.org/10.1016/0097-3165(81)90058-3openalex-snapshot
A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
inferredcites →https://doi.org/10.1016/0097-3165(83)90005-5openalex-snapshot
The unique 3-neighborly 4-manifold with few vertices
inferredcites →https://doi.org/10.1016/s0195-6698(80)80017-5openalex-snapshot
The Minimum Number of Faces of a Simple Polyhedron
inferredcites →https://doi.org/10.1016/s0195-6698(81)80037-6openalex-snapshot
The Numbers of Faces of Polytope Pairs and Unbounded Polyhedra
inferredcites →https://doi.org/10.1016/s0304-0208(08)72824-xopenalex-snapshot
Weakly Saturated Graphs are Rigid
inferredcites →https://doi.org/10.1080/00029890.1981.11995175openalex-snapshot
Rigid and Flexible Frameworks
inferredcites →https://doi.org/10.1090/s0002-9904-1970-12601-5openalex-snapshot
Polytopes, graphs, and complexes
inferredcites →https://doi.org/10.1090/s0002-9947-1978-0492298-1openalex-snapshot
3-Pseudomanifolds with Preassigned Links
inferredcites →https://doi.org/10.1090/s0002-9947-1978-0511410-9openalex-snapshot
The Rigidity of Graphs
inferredcites →https://doi.org/10.1090/s0002-9947-1984-0752486-6openalex-snapshot
Infinitesimally Rigid Polyhedra. I. Statics of Frameworks
inferredcites →https://doi.org/10.1112/s002557930000245xopenalex-snapshot
On acyclic simplicial complexes
inferredcites →https://doi.org/10.1112/s0025579300005520openalex-snapshot
A generalized lower‐bound conjecture for simplicial polytopes
inferredcites →https://doi.org/10.1112/s0025579300008500openalex-snapshot
Properties and characterizations of k ‐trees
inferredcites →https://doi.org/10.2140/pjm.1961.11.431openalex-snapshot
On the graph structure of convex polyhedra inn-space
inferredcites →https://doi.org/10.2140/pjm.1973.46.349openalex-snapshot
A proof of the lower bound conjecture for convex polytopes
inferredcites →https://doi.org/10.2140/pjm.1975.57.33openalex-snapshot
Generalized combinatorial cells and facet splitting
inferredcites →https://doi.org/10.2307/2373013openalex-snapshot
Tightly Embedded 2-Dimensional Polyhedral Manifolds
inferredcites →https://doi.org/10.2969/aspm/01110187openalex-snapshot
Generalized $H$-Vectors, Intersection Cohomology of Toric Varieties, and Related Results
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Enumerative problems for arborescences and monotone paths on polytope graphs
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A Homological Interpretation of Skeletal Rigidity
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On Traces ofd-stresses in the Skeletons of Lower Dimensions of Piecewise-lineard-manifolds
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Inner Diagonals of Convex Polytopes
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Empty Simplices of Polytopes and Graded Betti Numbers
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Rigidity and the Lower Bound Theorem for Doubly Cohen–Macaulay Complexes
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A Tale of Centrally Symmetric Polytopes and Spheres
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Acute Geodesic Triangulations of Manifolds
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Designing Optimization Problems with Diverse Solutions
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Combinatorics with a Geometric Flavor
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Flag Numbers and FLAGTOOL
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Combinatorics and Convexity
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Balanced Manifolds and Pseudomanifolds
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Face enumeration on simplicial complexes
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Generalized Stress and Motions
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Face Numbers and Subdivisions of Convex Polytopes
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Some Aspects of the Combinatorial Theory of Convex Polytopes
inferred← citeshttps://doi.org/10.1007/bf01299302openalex-snapshot
Rigidity and the Alexandrov-Fenchel inequality
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On low-dimensional faces that high-dimensional polytopes must have
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Lower-bound theorems for pseudomanifolds
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P.L.-Spheres, convex polytopes, and stress
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A Proof of KÜhnel’s Conjecture for n ⩾ k2 + 3k Eric Sparla
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An Upper and a Lower Bound Theorem for Combinatorial 4-Manifolds
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On Flag Vectors, the Dowling Lattice, and Braid Arrangements
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Shellings and the Lower Bound Theorem
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Intersection homology of toric varieties and a conjecture of Kalai
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The Numbers of Edges of 5-Polytopes with a Given Number of Vertices
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Embeddings of Edge-Colored Dual Graphs of Balanced 3- and 4-Manifolds
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A Geometric Lower Bound Theorem
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An Inequality for Anti-self-polar Polytopes
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Relationships Among Flag f -Vector Inequalities for Polytopes
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Real Root Conjecture Fails for Five- and Higher-Dimensional Spheres
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Empty Simplices of Polytopes and Graded Betti Numbers
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Rigidity and the Lower Bound Theorem for Doubly Cohen-Macaulay Complexes
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Rigidity and the Lower Bound Theorem for Doubly Cohen–Macaulay Complexes
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Empty Simplices of Polytopes and Graded Betti Numbers
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On Kalai’s Conjectures Concerning Centrally Symmetric Polytopes
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Affine and Toric Hyperplane Arrangements
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Applications of Klee’s Dehn–Sommerville Relations
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Lower Bounds for Cubical Pseudomanifolds
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Rigidity and Volume Preserving Deformation on Degenerate Simplices
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A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes
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Complexity Yardsticks for f-Vectors of Polytopes and Spheres
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Vertex Spanning Planar Laman Graphs in Triangulated Surfaces
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A Lower Bound Theorem for Strongly Regular CW Spheres with up to $$2d+1$$ Vertices
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Affine Stresses: The Partition of Unity and Kalai’s Reconstruction Conjectures
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Three Theorems, with Computer-Aided Proofs, on Three-Dimensional Faces and Quotients of Polytopes
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On embeddability and stresses of graphs
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A Positive Answer to Bárány’s Question on Face Numbers of Polytopes
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Optimizing for strategy diversity in the design of video games
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Projective background of the infinitesimal rigidity of frameworks
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On r-stacked triangulated manifolds
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Isometric Embeddings in Imaging and Vision: Facts and Fiction
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On the generalized lower bound conjecture for polytopes and spheres
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Balanced complexes and complexes without large missing faces
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Face numbers and the fundamental group
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Strongly minimal triangulations of (S 3×S 1)#3 and (S 3 S 1)#3
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Tight combinatorial manifolds and graded Betti numbers
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Lifting degenerate simplices with a single volume constraint
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Graded Betti Numbers of Balanced Simplicial Complexes
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Simple convex polytopes and the strong Lefschetz theorem
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The extended f-vectors of 4-polytopes
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A new basis of polytopes
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Skeletal rigidity of simplicial complexes, II
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Skeletal rigidity of simplicial complexes, I
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Combinatorial Aspects of Convex Polytopes
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Polyhedral Manifolds
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10.1016/b978-044488002-4/50020-8
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Lifting inequalities for polytopes
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Topological finiteness for edge-vertex enumeration
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Socles of Buchsbaum modules, complexes and posets
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Three-dimensional normal pseudomanifolds with relatively few edges
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Global rigidity of triangulated manifolds
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On Walkup’s class K(d) and a minimal triangulation of (S3S1)#3
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Normal surfaces as combinatorial slicings
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On k -stellated and k -stacked spheres
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The rigidity of the graphs of homology spheres minus one edge
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A characterization of normal 3-pseudomanifolds with at most two singularities
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Topological and combinatorial characterizations of normal 3-pseudomanifolds with g2 ≤ 5
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Rigid frameworks with dilation constraints
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On a construction of some homology d-manifolds
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Tight triangulations of closed 3-manifolds
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Lower bound theorems for general polytopes
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Stable sets in flag spheres
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Lower bound theorem for normal pseudomanifolds
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Minimal triangulations of sphere bundles over the circle
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A characterization of simplicial polytopes with g2=1
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Stacked polytopes and tight triangulations of manifolds
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An infinite family of tight triangulations of manifolds
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Separation index of graphs and stacked 2-spheres
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A characterization of homology manifolds with g2≤ 2
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Volume rigidity and algebraic shifting
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On the number of simplices required to triangulate a Lie group
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Tight Submanifolds, Smooth and Polyhedral
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Rigidity of symmetric simplicial complexes and the lower bound theorem
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A Construction Principle for Tight and Minimal Triangulations of Manifolds
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Higher chordality: From graphs to complexes
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An upper bound problem for triangulations of manifolds
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Infinitesimally Rigid Polyhedra. II: Modified Spherical Frameworks
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Projected products of polygons
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Torus Actions and Their Applications in Topology and Combinatorics
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Affine Stresses, Inverse Systems, and Reconstruction Problems
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Face Numbers of Manifolds with Boundary
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Gorenstein rings through face rings of manifolds
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LOWER BOUND THEOREMS AND A GENERALIZED LOWER BOUND CONJECTURE FOR BALANCED SIMPLICIAL COMPLEXES
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Fair Division and Generalizations of Sperner- and KKM-type Results
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Rigidity of Balanced Minimal Cycle Complexes
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Systolic inequalities for the number of vertices
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Combinatorics of 4-dimensional resultant polytopes
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Face Numbers of Polytopes and Complexes
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On the numbers of faces of low-dimensional regular triangulations and shellable balls
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How many simplices are needed to triangulate a Grassmannian?
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Constructions and obstructions for extremal polytopes
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Incidence Graphs and Unneighborly Polytopes
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Linear constraints on Face numbers of Polytopes
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Additive structures on f-vector sets of polytopes
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On linkages in polytope graphs
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Minimal flag triangulations of lower-dimensional manifolds
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Rigidity through a Projective Lens
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The Fundamental Group of Balanced Simplicial Complexes and Posets
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Remarks on Missing Faces and Generalized Lower Bounds on Face Numbers
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Average Betti Numbers of Induced Subcomplexes in Triangulations of Manifolds
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Almost Simplicial Polytopes: The Lower and Upper Bound Theorems
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Euler's polyhedron formula — a starting point of today's polytope theory
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Face enumeration—from spheres to manifolds
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H-vectors of simplicial complexes with Serre’s conditions
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Remarks on the Combinatorial Intersection Cohomology of Fans
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A characterization of simplicial polytopes with g_2=1
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On Walkup's class ${\cal K}(d)$ and a minimal triangulation of $(S^3 \times \rotatebox{90}{\ltimes} S^1)^{\#3}$
inferred← citeshttps://doi.org/10.48550/arxiv.0809.0088openalex-snapshot
Generalized asymptotic Euler's relation for certain families of polytopes
inferred← citeshttps://doi.org/10.48550/arxiv.0910.0042openalex-snapshot
Lower Bounds for Cubical Pseudomanifolds
inferred← citeshttps://doi.org/10.48550/arxiv.1207.6182openalex-snapshot
Tight triangulations of some 4-manifolds
inferred← citeshttps://doi.org/10.48550/arxiv.1411.0987openalex-snapshot
Thirty-five years and counting
inferred← citeshttps://doi.org/10.48550/arxiv.1506.00447openalex-snapshot
Tight and stacked triangulations of manifolds
inferred← citeshttps://doi.org/10.48550/arxiv.1508.00159openalex-snapshot
On the cohomology of moment-angle complexes associated to Gorenstein* complexes
inferred← citeshttps://doi.org/10.48550/arxiv.1510.08258openalex-snapshot
Almost simplicial polytopes I. The lower and upper bound theorems
inferred← citeshttps://doi.org/10.48550/arxiv.1607.05757openalex-snapshot
A characterization of homology manifolds with $g_2\leq 2$
inferred← citeshttps://doi.org/10.48550/arxiv.1608.06274openalex-snapshot
Homological combinatorics and extensions of the cd-index
inferred← citeshttps://doi.org/10.48550/arxiv.1706.03322openalex-snapshot
The face numbers of homology spheres
inferred← citeshttps://doi.org/10.48550/arxiv.1709.02021openalex-snapshot
Additive structures on $f$-vector sets of polytopes
inferred← citeshttps://doi.org/10.48550/arxiv.1711.07218openalex-snapshot
Lefschetz and Lower Bound theorems for Minkowski sums
inferred← citeshttps://doi.org/10.48550/arxiv.1812.10454openalex-snapshot
Combinatorial Lefschetz theorems beyond positivity
inferred← citeshttps://doi.org/10.48550/arxiv.1909.06729openalex-snapshot
$g$-vectors of manifolds with boundary
inferred← citeshttps://doi.org/10.48550/arxiv.2003.13125openalex-snapshot
Estimate of number of simplices of triangulations of Lie groups
inferred← citeshttps://doi.org/10.48550/arxiv.2004.03362openalex-snapshot
Cohomological rigidity of manifolds with torus actions: I
inferred← citeshttps://doi.org/10.48550/arxiv.2012.14380openalex-snapshot
A complete characterization of $(f_0, f_1)$-pairs of 6-polytopes
inferred← citeshttps://doi.org/10.48550/arxiv.alg-geom/9704014openalex-snapshot
Intersection Homology of Toric Varieties and a Conjecture of Kalai
inferred← citeshttps://doi.org/10.48550/arxiv.math/0110277openalex-snapshot
Crepant Resolutions of Gorenstein Toric Singularities and Upper Bound Theorem
inferred← citeshttps://doi.org/10.48550/arxiv.math/0208073openalex-snapshot
Face numbers of 4-Polytopes and 3-Spheres
inferred← citeshttps://doi.org/10.48550/arxiv.math/0404465openalex-snapshot
Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres
inferred← citeshttps://doi.org/10.48550/arxiv.math/0407042openalex-snapshot
Projected Products of Polytopes
inferred← citeshttps://doi.org/10.48550/arxiv.math/0411009openalex-snapshot
Embeddability and Stresses of Graphs
inferred← citeshttps://doi.org/10.48550/arxiv.math/0411400openalex-snapshot
Convex Polytopes: Extremal Constructions and f-Vector Shapes
inferred← citeshttps://doi.org/10.48550/arxiv.math/0506372openalex-snapshot
Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
inferred← citeshttps://doi.org/10.48550/arxiv.math/0511751openalex-snapshot
Constructions for 4-Polytopes and the Cone of Flag Vectors
inferred← citeshttps://doi.org/10.48550/arxiv.math/0607396openalex-snapshot
On braxtopes, a class of generalized simplices
inferred← citeshttps://doi.org/10.5802/alco.121openalex-snapshot
g -vectors of manifolds with boundary
inferred← citeshttps://doi.org/10.7146/math.scand.a-15204openalex-snapshot
Face numbers of pseudomanifolds with isolated singularities
inferred← citeshttps://doi.org/10.7146/math.scand.a-23297openalex-snapshot
Stellar Theory for Flag Complexes
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